Autumn.wmf (12088 bytes) Concepts of Biology (BIOL116) - Dr. S.G. Saupe; Biology Department, College of St. Benedict/St. John's University, Collegeville, MN 56321;;

Ecology: Population Biology

I.  Introduction to Ecology

A.  Oikos
    Greek for home (therefore, literally = study of the home). Or, more appropriately, study of interactions between organisms and their environment

B.  Hierarchy of Organization.
    Ecologists typically study the level of population and above (e.g., population community ecosystem biosphere).  Note:  the scale can vary, depending on your perspective (we'll use a variety of examples including dung, our classroom, and the earth.

II.  What is a Population?

III.  Population Growth

A.  Natality, Mortality and Moving Around (migration)

Population growth is affected by: (1) birth rate (natality); (2) death rate (mortality); (3) immigration (entering a population from the outside); and (4)
emigration (exiting a population).  Thus:

population growth = (birth + immigration) - (death + emigration)

If we consider a closed population (ignoring immigration and emigration), then when... 

  • B > D the population grows

  • B < D the population shrinks 

  • B = D the population is stable (ZPG)

B.  The Persian Courtier story
    There is an old Persian legend that a courtier presented a beautiful chessboard to his king.  The king was so grateful that he asked what he could give him in return.  The courtier requested that the king give him 1 grain of rice for the first square on the board, double the amount to two grains for the second square, double it again to 4 grains for the third and so on.  The king readily agreed and ordered rice to be brought from the royal storeroom.  How many grains would the King have to give for the first 15 squares?  (click here for answer). 

    If we plot grains of rice vs. square number, what is the appearance of the graph?  Answer:  we would observe a "J curve" which is characteristic of exponential (logarithmic) relationships.  We can demonstrate this by plotting the log of the grains of rice vs. square number; this will result in a straight line.  An exponential graph/relationship is one that is doubling or tripling at each interval.

     What if the King tripled the rice for every square, how would graph appear?  What if he only gave rice every other square? or what if he started with 100 grains of rice instead of one?  How would the graph differ in each of these cases? 

C.  Theoretical population growth.
   This is similar to the Persian story.  The theoretical growth of a population, or rice in our royal story, can be mathematically expressed as:

G = rN   where 

  • G = growth rate of the population (dN/dt)

  • N = number of individuals at time t; 

  • r = net reproductive per individual, or the biotic potential (e.g., birth - death).  The biotic potential is influenced by factors such as age of first reproduction, number of offspring per reproduction, fraction of lifespan capable of reproduction.  

    Natural populations should theoretically grow at an exponential rate like rice on a checkerboard.  Consider a bacterial or yeast cell that divides every 20 minutes.  After 40 minutes there would be 4 bacteria.  After 60 minutes, 8, and so on.  

D.  Modeling Theoretical Growth - Populus.  
    Populus is a computer program written by Dr. Don Alstad (Univ. Minnesota) that, among other things, models the effect of various variables on exponential growth.  You can download the program and run it on your own computer.  In class, we will run some simulations with the program to answer the questions: 

  1. What is the effect on population growth (J-curve) of changing the initial number of individuals in the population? 

  2. What is the effect on population growth of changing the growth rate of the population?

E.  Population growth is constrained.  
     Natural populations only grow exponentially for a short period of time.  They do not maintain their exponential rate of growth indefinitely.  How do we know?  If they did, then the surface of the earth would be covered with bacteria from our single bacterial cell after about a week.  Or, consider elephants.  I believe it was Darwin who once calculated that a single pair of elephants would produce enough descendants in 100,000 years to fill the known universe.  In fact, the elephant population would be increasing so rapidly that they would expand off the surface of the earth at a speed approaching that of light. Cool.  But, since we obviously are not knee deep in bacteria nor do we have to dodge lightening elephants, populations clearly do not maintain their theoretically maximum rate of growth.  It's not surprising that the King went went broke - there was not enough rice to pay the courtier!

F.  Actual Population Growth.
Consider the actual growth of a population of yeast in a culture flask. (click here for data).  If we plot the number of yeast cells vs. time the graph will appears like an "S" or sigmoidal.  This is called a logistic curve or S-curve or sigmoidal curve and it represents the growth of natural populations under normal constraints. Study the curve and note:  

  1. Carrying Capacity - this is the maximum number of individuals of a population that occupy a given habitat.  It is symbolized by the letter "K" and represents the maximum number of individuals that can be sustained under the specified conditions.  At K, mortality equals natality.  

  2. Regions of the curve - lag phase, acceleration phase, inflection point (pt of maximum growth rate), deceleration phase, steady state (= K)

  3. Environmental resistance - refers to the factors that constrains population growth and that prevent a population from achieving its theoretical maximum (it is essentially the difference between the S and J curves)

  4. Comparison of S and J curves.  Note that they are similar at low population density.  As the population increases, the curves diverge more.  The divergence is a measure of environmental resistance.  Thus, population growth levels off at K because of environmental resistance.  Environmental resistance can be density independent or density dependent.

G.  Environmental Resistance - Density-dependent population controls.
   These are factors whose magnitude is dependent on the size of the population.  They include:

  1. resource availability (e.g., food, space, water); 

  2. waste production/toxic byproducts (e.g., yeast and alcohol); 

  3. intra-specific (between individuals of a species) competition (e.g., planting veggies in a garden too closely results in spindly, low-yielding plants); 

  4. inter-specific (between species) competition (e.g., between crops and weeds).; 

  5. emigration - often caused by increased crowding, stimulates physiological/behavioral changes (e.g., aphids, lemmings).  In aphids, the females are normally wingless but sprout wings under crowding conditions; 

  6. stress (abnormal behaviors and decreased reproductive output related to overcrowding).  Shown in rats, not primates; and 

  7. increased predation and parasitism (major source of mortality for many populations). 

H.  Environmental Resistance - Density-independent population controls 
    These operate irrespective of the size of the population.  The magnitude of the effect is not related to the size of the population (
e.g., fire, drought, landslides, earthquakes, temperature).  These are primarily abiotic (= non-living factors).

I.  The S curve, or logistic curve
Can be mathematically represented by modifying the exponential growth equation by adding a term [(K-N)/K] for environment resistance. Thus, the equation is:  G = rN((K-N)/K).  When N is small (low population density), then the term for environmental resistance is near one, and the population growth approaches the exponential level. Check the graph and note the similarity in early S and J curves.  If N is large, then the environmental resistance term approaches zero, therefore there is large environmental resistance, and population growth approaches zero.  

J.  Modeling Logistic Growth - Populus
Once again, let's use Populus to simulate the growth of a population in response to changes in K, N and r.  We will answer the following questions:

  1. What is the effect on logistic growth of changing K?

  2. What is the effect on logistic growth of changing N?

  3. What is the effect on logistic growth of changing r?

K. Population growth patterns & carrying capacity
The growth of a population may approach the carrying capacity:

  1. smoothly as in yeast and other microbes grown in a culture flask;

  2. oscillate around the carrying capacity; or

  3. exhibit a population explosion followed by a crash (boom and bust).  

  4. The population explosion can be caused by...

    (a) decreased environmental resistance. This could happen if abundant resources become available.  For example, in lakes a population boom is often associated with increased releases of phosphorus, or decreased predation.  For example, the introduction of rabbits to Australia in 1859 resulted in a huge population explosion since there were no natural predators. To kill the rabbits, a virus (Myxoma) that was transmitted by a mosquito vector was introduced; or

    (b) overuse of resources such as food, space; or

    (c) increased environmental degradation.


  5. If severe, the population crash can result in extinction. 

IV.  Factors other than growth/size that influence/characterize a population

A.  Density (number of individuals per unit area or unit volume) (not covered in class or on exam)  
    Two extremes: those that prefer survival at low population density, called r-selected, and those that prefer survival of high population density, called K-selected.  Called "K" because these populations are maintained at high density, at/near the carrying capacity (K).  The r-selected species are maintained at lower density, near the lag phase of the J/S curve, where the biotic potential (r) is high. 

    Species that are r-selected are typically small; have a short life span; occupy disturbed, unpredictable environments; have a high reproductive potential (produce lots of small offspring early in their life cycle); invest little parental care (typically type III survivorship curve); and are "opportunistic" or "weedy" species.   K selected species exhibit contrasting characteristics.  Table 1 summarizes the differences between r-selected and K-selected species

Table:  Comparison of r vs. K strategy
  r-Strategy K-strategy
Population Density - Survival at low vs. high density low hi
Population Density - survival near K or rmax rmax near K
Species type (opportunistic vs. equilibrium) opportunistic species ("weedy") equilibrium species
Habitat Preference - disturbed vs. undisturbed disturbed undisturbed
Habitat Preference - stable vs. unpredictable  unpredictable stable, predictable
Habitat Preference constant vs. variable  variable constant
Successional Community early  late 
Growth Curve

boom and bust pattern

S curve
Reproductive Strategy - Offspring size (small vs. large) small large
Reproductive Strategy - time of reproduction (early vs. late) early late
Reproductive Strategy - Offspring Number (few vs. many) many few
Parental investment in offspring (little, large) little  large
Organism size (small vs. large) small large
life cycle (long vs. short) short 


Strategy (quality vs. quantity)


Survivorship Curve (I, II or III) Type III 

Type I, II 

 B.  Distribution (dispersion) in space. 
    Must sample populations - portion that represents the whole.  Various types including mark & recapture. 
Three major patterns:

  1. Random - rare (e.g. flour beetles in the lab);

  2. Clumped - common because: (a) environment is usually not uniform but patchy, (b) individuals often occur in a social group, such as fish in a school or clumps of aspen trees; and (c) limited dispersal of offspring; 

  3. Uniform - not common, the result of competition. e.g. nesting seabirds, prairie dogs, creosote bush (allelopathy, seed predation by rodents)

    Note:  spatial distribution patterns for a population can change over time.  For example,  young sand pine populations are initially clumped but become more uniform as the population ages.

C.  Distribution in time  

1.  temporal differences in species, e.g., seasonal fluctuations.  

2.  Survivorship curves.  Type I, II, III.
    Refers to the number of survivors of a population after a given period of time - just like the TV show! Life tables are used to summarize patterns of life and death; follows a cohort of individuals.  If we plot % survivors vs. time there are three basic patterns:

  • Type I - most individuals reach physiological age, little infant mortality, lot of maternal care (e.g., humans)

  • Type II - constant mortality (e.g., many animals; including the TV show cast)

  • Type III - hi infant mortality, little maternal care (e.g., plants, many invertebrates, fish)

3.  Age structure pyramids.
    Measure of frequency of individuals of a particular age in the population.  Influenced by life span, life expectancy, age of first reproduction.  Used to predict future growth of the population.  Check it out in the text.

D.  Disturbances - short term events that influence population density; these can be density dependent or independent.

V.  Human Population Growth.

  1. ZPG video - Human population growth.  Check out the questions in the Population Study Guide (click here) 

  2. Does the human population have a carrying capacity?  Cornucopians, like Julian Simon say "no"; Neo-Malthusians, like Paul/Anne Ehrlich say "YES".  Assume there is a carrying capacity, what is it?  and when will we attain it

  3. How to control human population growth? Possible ideas:  (a) increase family planning efforts, including delaying reproduction; (b) improve economic standards (i.e., demographic transition model - high birth rates usually accompany pre-industrial countries).

VI.  Life History
    Patterns of growth, development, reproduction, etc., can affect population growth.  Tradeoffs exist between numbers and size of offspring and parental care; between growth and reproduction, etc.  Can determine how heavily a population is exploited (e.g., whales) and to control populations.

Evolution of populations.  (not on exam)
Guppies in streams in Trinidad.  Pike prey on large ones.  Killifish prey on smaller ones.  Streams with pike have smaller guppies and streams with killifish have larger guppies.  Both strategies minimize the chances of getting eaten.  These differences are heritable (can be passed to offspring).  Demonstrated in the lab and field.

VII.  References:

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Last updated: March 30, 2004        � Copyright by SG Saupe